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Day 38: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Sets. This type asked 3 times: CDS 2 2018, CDS 1 2020, CDS 2 2024. This one: CDS 2 2024 See all 3 of this type

    34
    In a class containing 200 students, nn students prefer both tea and coffee; 2n2n students prefer coffee, 3n3n students prefer tea; 4n4n students prefer neither tea nor coffee. What is the value of nn ?

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  2. Question 2

    Surds, Indices and Simplification. This type asked 3 times: CDS 2 2020, CDS 1 2022, CDS 2 2024. This one: CDS 1 2022 See all 3 of this type

    8
    What is the value of the following? 154+45+165+56+176+67+187+78+198+89\frac{1}{5\sqrt{4} + 4\sqrt{5}} + \frac{1}{6\sqrt{5} + 5\sqrt{6}} + \frac{1}{7\sqrt{6} + 6\sqrt{7}} + \frac{1}{8\sqrt{7} + 7\sqrt{8}} + \frac{1}{9\sqrt{8} + 8\sqrt{9}}

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  3. Question 3

    Time, Speed and Distance. This type asked 3 times: CDS 1 2018, CDS 1 2023, CDS 2 2024. This one: CDS 2 2024 See all 3 of this type

    9
    Train XX crosses a man standing on the platform in 24 seconds and train YY crosses a man standing on the platform in 18 seconds. They cross each other while running in opposite directions in 20 seconds. What is the ratio of speed of XX to speed of YY ?

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  4. Question 4

    Trigonometric Ratios and Identities. This type asked 3 times: CDS 2 2018, CDS 1 2022, CDS 2 2024. This one: CDS 2 2024 See all 3 of this type

    14
    If 0≤(α−β)≤(α+β)≤π20 \le (\alpha - \beta) \le (\alpha + \beta) \le \frac{\pi}{2}, tan⁡(α+β)=3\tan(\alpha + \beta) = \sqrt{3} and tan⁡(α−β)=13\tan(\alpha - \beta) = \frac{1}{\sqrt{3}}, then what is tan⁡α⋅cot⁡2β\tan\alpha \cdot \cot 2\beta equal to ?

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  5. Question 5 (case study, 2 parts)

    Mensuration 2D. This type asked 3 times: CDS 2 2018, CDS 1 2020, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    Consider the following for the next two (02) items that follow : Let ABCD be the diameter of a circle of radius 6 cm. The lengths AB, BC and CD are equal. Semi-circles are drawn with AB and BD as diameters as shown in the figure given below.
    99
    What is the ratio of the area of the shaded region to that of the non-shaded region ?

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    100
    What is the perimeter of the shaded region ?

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